Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#23603 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C24×C17 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C23×C4×C17 ◁ G | |
970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,28,31,27,32,26,40)(24,33,42,44,35,50,36,29)(25,30,41,46,39,47,38,48)(34,49,52,43,51,45,37,53);(18,19)(20,21)(22,24,26,36,27,35,28,42)(23,29,31,33,32,44,40,50)(25,37,38,51,39,52,41,34)(30,45,46,53,47,49,48,43);(19,21)(22,25,27,39)(23,30,32,47)(24,34,35,51)(26,41,28,38)(29,43,44,53)(31,48,40,46)(33,49,50,45)(36,52,42,37);(24,35)(29,44)(33,50)(34,51)(36,42)(37,52)(43,53)(45,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 16591);